GCF of 5742/585, 5814/121
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5742/585, 5814/121 i.e 18/70785 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5742/585, 5814/121.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 5742/585,5814/121?
Given fractions are 5742/585,5814/121
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 5742/585,5814/121, numerators are 5742,5814
Denominators are 585,121
The GCF of 5742,5814 is 18 .
LCM of 585,121 is 70785.
The greatest common factor of 5742/585,5814/121 = [GCF of 5742,5814]/[LCM of 585,121]= 18/70785
Therefore, the GCF of 5742/585,5814/121 is 18/70785.
To find the highest common factor of 5742,5814, we have to find the factors of both numbers and list the highest common factor.
The factors of 5742 are 1, 2, 3, 6, 9, 11, 18, 22, 29, 33, 58, 66, 87, 99, 174, 198, 261, 319, 522, 638, 957, 1914, 2871, 5742
The factors of 5814 are 1, 2, 3, 6, 9, 17, 18, 19, 34, 38, 51, 57, 102, 114, 153, 171, 306, 323, 342, 646, 969, 1938, 2907, 5814
The HCF of 5742,5814 is 18.
Lets's calculate GCF of 5742,5814
| 2 | 5742, 5814 |
| 3 | 2871, 2907 |
| 3 | 957, 969 |
| 319, 323 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 5742,5814 By Matching Biggest Common Factor Method
Now, list down the factors of 5742
:1,2,3,6,9,11,18,22,29,33,58,66,87,99,174,198,261,319,522,638,957,1914,2871,5742
Now, list down the factors of 5814
:1,2,3,6,9,17,18,19,34,38,51,57,102,114,153,171,306,323,342,646,969,1938,2907,5814
Greatest Common Factor
We found the factors 5742,5814 . The biggest common factor number is the GCF number.
So the greatest common factor 5742,5814 is 18.
Lets's calculate LCM of 585,121
Given numbers has no common factors except 1. So, there LCM is their product i.e 70785
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/70785
Therefore, the GCF of Fractions 5742/585,5814/121 is 18/70785
Least Common Multiple of 585,121 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 585,121 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(585,121) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(585,121) x common factors =1 x 1 = 1
LCM(585,121) = ( 585 × 121 ) / 1
LCM(585,121) = 70785 / 1
LCM(585,121) = 70785
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FAQs on GCF of Fractions of 5742/585, 5814/121
1. What is the HCF of 5742,5814?
The HCF of 5742,5814 is 18
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 5742/585, 5814/121?
Answer: GCF of Numerators as per given numbers 5742/585, 5814/121 is
GCF of Numerators i.e. for 5742,5814 is 18
LCM of denominators i.e. for 585,121 is 70785.
Thus, GCF of Fractions is 18/70785.Finally, GCF of Fractions for 5742/585, 5814/121 is 18/70785.